hi folks please i need help for this question Given a one to

hi folks,

please i need help for this question. Given a one to one and onto function with its inverse function. what is the composition of the function and its inverse will equal to?

Solution

Let, f be a function from R to R

Let,

f(x)=2x

f(x)=f(y) means

2x=2y ie x=y

So, f is one to one

For any y in R

f(y/2)=y

So, f is onto

f(f(y))=2f(y)=4y

f^{-1}(x)=x/2